FIRST HALF

Guardiola's last training session as **FC Barcelona**'s coach. They've been
training for 2 hours preparing the final of the Spanish Cup, and **Pep Guardiola** proposes to them the last **exercise** before going
to the changing room.

**Guardiola** picks up to four players to **cross the football field** from goal to goal passing the ball one each other
without dropping it. The four players must leave the same goal area and arrive to the other one. They have **17 minutes** to get everyone
to the opposite goal. They only have one ball, which will be carried from one goal to the other one. They can cross the field **one by one**
(kicking softly the ball without dropping it), or **by pairs** (passing the ball from one to the other one without touching the ground).
They can't kick the ball from one area to another, but a player must **return** with it, touching it the manner described. Evidently, some
of the players are more skillful than others in handling the ball, so that when two players go together, they will be always crossing the field at the **slower speed**

The data are as follows:

**Messi**: takes **1 minute** to cross the field kicking the ball.

**Iniesta**: takes **2 minutes**.

**Cesc**: takes **5 minutes**.

** Piqué**: takes

For example, if **Messi** and **Cesc** cross together the field by passing each other the ball,
it takes **5 minutes**. Then the ball can be returned by **Cesc**, and we'll have **10 minutes**
elapsed from the beginning. Then **Cesc** and **Piqué** cross together... and so on with all of them.

...

With this data, which **strategy** should use all the players to **cross ** from one goal area to the other one in just **17 minutes**?

It's worth thinking about it for some minutes, before going to the solution area. And I promise there's no cheating.

The **solution** is as follows:

1. **Messi** and **Iniesta** cross the field at first. It takes a total of 2 minutes.

2. **Iniesta** returns. 4 minutes are consumed.

3. Now **Cesc** and **Piqué** cross the field. It takes them 10 minutes, so that we have
a total of 14 minutes.

4. **Messi** returns with the ball. It takes 1 minute, so we totalize 15 minutes.

5. And finally, **Iniesta** and **Messi** return again with the ball. It takes 2 minutes to
cross, so we get the total of 17 minutes.

You've probably tried more than once with **Cesc** and **Piqué**
crossing the field together, but the problem was that afterwards **one of them had to return**,
and the time increases exponentially. The solution was in sight: we must return with one of the two quicker
players we have, but that means that we need both of them at the opposite goal. The first player, in order to return
with the ball after the first trip, and second one, to return the ball after the two slowest players have crossed
the field. In fact, the result is the same if, at first, we cross the field with **Messi**,
and then we use **Iniesta** for the fourth trip.

This is a perfect example of what is known as **'lateral thinking'**.
The funny thing is that as soon as you find the solution, you can't understand how you didn't happen it before.
And the difficulty is that you are unconsciously 'pushing' to go in one direction, and surprisingly that turns out wrong.

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